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Historical biogeography models with dispersal probability as a func7on of distance(s)
Nicholas J. Matzke, Postdoctoral Fellow, NIMBioS (Na6onal Ins6tute of Mathema6cal, www.nimbios.org) SSE symposium: Fron6ers in Parametric Biogeography 10:45 am, Nobre Room, Guarujá, Brasil, June 30, 2015
Figure: Map of stochas6cally-‐mapped dispersal events BioGeoBEARS model: BAYAREALIKE-‐d-‐e+a+x+n
Data from: Angiosperm megatree, Zanne et al. (2013, Nature)
Acknowledgements Ques6ons/comments/collabora6ons at: [email protected] (also: seeking a job!)
Funding: NIMBioS NSF “Bivalves in Time and Space” UC Berkeley Wang Fellowship UC Berkeley Tien Fellowship Google Summer of Code NIMBioS
TRY IT YOURSELF AT: hMp://phylo.wikidot.com/biogeobears
Thanks especially to: !Jim Albert !NIMBioS Brian O’Meara Jeremy Beaulieu Ka?e Massana Michael Landis !Ph.D. commicee John Huelsenbeck Tony Barnosky David Jablonski Roger Byrne !Systema?c Biology editors & reviewers
1. Historical biogeography: What’s the point? !
2. Models morghulis !
3. Models in BioGeoBEARS, and valida6on !
4. Adding more realism with +x and +n !
5. Es6ma6ng the global angiosperm macroevolu6onary dispersal kernel
Outline
Outline
1. Historical biogeography: What’s the point? !
2. Models morghulis !
3. Models in BioGeoBEARS, and valida6on !
4. Adding more realism with +x and +n !
5. Es6ma6ng the global angiosperm macroevolu6onary dispersal kernel
e.g. Hawaiian Psychotria
Tradi6onally, back to parsimony days, the point has been “Ancestral Area Reconstruc6on”
Historical biogeography: What’s the point?
e.g. Hawaiian Psychotria
Sugges7on: let’s replace…“Ancestral Area Reconstruc6on” with “Ancestral Range Es6ma6on” (credit: Brian Moore)
Historical biogeography: What’s the point?
Historical biogeography: What’s the point?Sugges7on: let’s replace…“Ancestral Area Reconstruc6on” with “Ancestral Range Es6ma6on” (credit: Brian Moore)
Historical biogeography: What’s the point?
Is Ancestral Range Es6ma6on the only point of historical biogeography? !Not originally. The original hope was that by looking at many taxa, we could infer common pacerns and processes. !(e.g.: General Area Cladograms, Lieberman-‐modified Brooks Parsimony Analysis)
Historical biogeography: What’s the point?
I think sta6s6cal model choice can bring process back into historical biogeography in a big way. !We can do this by implemen6ng different models and seeing what probability they confer on the data (the likelihood). !We don’t expect this to be perfect, of course, but it is becer than just picking one model and not tes6ng it. -‐ Already standard procedure in PCMs.
“All models are wrong, but some models are useful.”
George Box
George E. P. Box(1919-2013)!
This phrase is ubiquitous, but s6ll not kept in mind enough. !
Perhaps drama6za6on will help…
For drama, look no further than…
HBO, 9 pm Sundays
In the free city of Braavos, the tradi7onal gree7ng is:
In the free city of Braavos, the tradi7onal gree7ng is:
The Faceless Man, Jaqen H'ghar!
In the free city of Braavos, the tradi7onal gree7ng is:
George E. P. Box(1919-2013)!
George E. P. Box(1919-2013)!
George E. P. Box(1919-2013)!
MODELS
MODELS
MODELS
MODELS
George E. P. Box(1919-2013)!
MODELS
MODELS
MODELS
MODELS
The Faceless Man Jaqen H'ghar!
George E. P. Box(1919-2013)!
MODELS
MODELS
MODELS
MODELS
The Faceless Man Jaqen H'ghar!
Models doeharis: All models must serve
!
Let’s make that happen with model comparison in
BioGeoBEARS
1. Historical biogeography: What’s the point? !
2. Models morghulis !
3. Models in BioGeoBEARS, and valida6on !
4. Adding more realism with +x and +n !
5. Es6ma6ng the global angiosperm macroevolu6onary dispersal kernel
Outline
Model comparison in BioGeoBEARS
Example: DEC vs. DEC+J on Hawaiian Psychotria
DEC LnL = -‐34.5 DEC+J LnL = -‐20.9
(tree & geog: Ree & Smith 2008)
(for the +* model, set include_null_range=FALSE)
DEC* LnL = -‐22.28 DEC*+J LnL = -‐20.49
Model comparison in BioGeoBEARS
(tree & geog: Ree & Smith 2008)
Example: DEC* vs. DEC*+J on Hawaiian Psychotria !
(for the * model, set include_null_range=FALSE)
Model comparison in BioGeoBEARS
LnL d e j
DEC -34.5 0.034 0.28 0
DEC+J -20.9 0 0 0.11
DEC* -22.28 0.16 11.7(+) 0
DEC*+J -20.5 0 14(+) 0.12
Figure 1, Matzke 2013, Frontiers of Biogeography
Figure 1, Matzke 2013, Frontiers of Biogeography
Figure 1, Matzke 2013, Frontiers of Biogeography
Figure 1, Matzke 2013, Frontiers of Biogeography
Figure 1, Matzke 2013, Frontiers of Biogeography
Figure 1, Matzke 2013, Frontiers of Biogeography
Figure 1, Matzke 2013, Frontiers of Biogeography
Figure 1, Matzke 2013, Frontiers of Biogeography
Figure 1, Matzke 2013, Frontiers of Biogeography
Figure 1, Matzke 2013, Frontiers of Biogeography
Figure 1, Matzke 2013, Frontiers of Biogeography
Figure 1, Matzke 2013, Frontiers of Biogeography
Figure 1, Matzke 2013, Frontiers of Biogeography
Figure 1, Matzke 2013, Frontiers of Biogeography
DEC (LAGRANGE)
Figure 1, Matzke 2013, Frontiers of Biogeography
DEC (LAGRANGE)
Figure 1, Matzke 2013, Frontiers of Biogeography
DEC (LAGRANGE)
Which model
should we use?
Figure 1, Matzke 2013, Frontiers of Biogeography
DEC (LAGRANGE)
Model comparison in BioGeoBEARS
DEC DEC+J
Model comparison in BioGeoBEARS
DEC DEC+J !
DIVALIKE DIVALIKE+J
Model comparison in BioGeoBEARS
DEC DEC+J !
DIVALIKE DIVALIKE+J !
BAYAREALIKE BAYAREALIKE+J
Model comparison in BioGeoBEARS
DEC DEC+J !
DIVALIKE DIVALIKE+J !
BAYAREALIKE BAYAREALIKE+J
DEC* DEC*+J !
DIVALIKE* DIVALIKE*+J !
BAYAREALIKE* BAYAREALIKE*+J
Model comparison in BioGeoBEARS
Across 14 datasets:!!Caecilians!Cyrtandra!Salamanders!Leafhoppers!Lonicera!Drosophila!Honeycreepers!Megalagrion!Orsonwelles!Palpimanoid spiders!Psychotria!Plantago!Scaptomyza!Silverswords!
AIC model weights across 14 datasets (assembled in Massana, Beaulieu, Matzke, O’Meara, in prep.)
(mostly island datasets from Matzke 2014)
What corresponds to the 3 models in RASP?
Across 14 datasets:!!Caecilians!Cyrtandra!Salamanders!Leafhoppers!Lonicera!Drosophila!Honeycreepers!Megalagrion!Orsonwelles!Palpimanoid spiders!Psychotria!Plantago!Scaptomyza!Silverswords!
AIC model weights across 14 datasets (assembled in Massana, Beaulieu, Matzke, O’Meara, in prep.)
(mostly island datasets from Matzke 2014)
Across 14 datasets:!!Caecilians!Cyrtandra!Salamanders!Leafhoppers!Lonicera!Drosophila!Honeycreepers!Megalagrion!Orsonwelles!Palpimanoid spiders!Psychotria!Plantago!Scaptomyza!Silverswords!
AIC model weights across 14 datasets (assembled in Massana, Beaulieu, Matzke, O’Meara, in prep.)
(mostly island datasets from Matzke 2014)
What corresponds to the 3 models in RASP?
Now we have 12 models. Is that the end?
Nope. !
Models morghulis. Models dohaeris. !
Figure 1, Matzke 2013, Frontiers of Biogeography
DEC (LAGRANGE)
Anagene7c range-‐switching parameter, a
In one sense, anagene6c range-‐switching is an absurd process (models morghulis) !
!
But, it might be a decent approxima6on, if jump dispersal is the main dispersal mode, but many lineages are ex6nct or unsampled (models dohaeris)
BAYAREALIKE*-‐d-‐e+aequals unordered character model
(island model)
a
BAYAREALIKE*-‐d-‐e+a is a model we can use for valida7on
BioGeoBEARS state
probabili6es
phytools state probabili6es (Revell)
Validate Biogeographical Stochas7c Mapping
BAYAREALIKE*-‐d-‐e+a is a model we can use for valida7on
BioGeoBEARS, distribu6on of many Biogeographical Stochas7c Maps
phytools state probabili6es (Revell)
Biogeographical Stochas7c Maps converge onstate probabili7es
DEC state probabili6es
BioGeoBEARS, distribu6on of many Biogeographical Stochas7c Maps
To make ClaSSE & DEC equivalent: !
DEC or DEC+J equals ClaSSE, *if*:
-‐ d and e control character change rates -‐ all ex6nc6on rates set to zero -‐ specia6on rate for each cladogenesis = (Yule rate) 6mes weight/sum(weights) -‐ subtract equilibrium probabili6es at the root
!
DEC, DEC+J (BioGeoBEARS) vs. ClaSSE (diversitree)
DEC, DEC+J (BioGeoBEARS) vs. ClaSSE (diversitree)
LnLs for: DEC-‐e = d DEC = e DEC+J = j
1. Historical biogeography: What’s the point? !
2. Models morghulis !
3. Models in BioGeoBEARS, and valida6on !
4. Adding more realism with +x and +n !
5. Es6ma6ng the global angiosperm macroevolu6onary dispersal kernel
Outline
One of the revolu6onary features of Lagrange was adding “manual dispersal modifiers” !
E.g., You might try a constrained model, where !
* dispersal from North America -‐> South America gets a mul6plier of 1 * dispersal from Africa -‐> South America gets a mul6plier of 0.1 * dispersal from Africa -‐> North America gets a mul6plier of 0.01
Standard approach: manual dispersal matrix
These mul6pliers are subjec6ve, but I think such constrained models are useful. !
If you get improvement, it indicates some improved fit between the phylogene6c da6ng, distribu6ons, and observed geography at the 6ps !
If LnL gets worse, it indicates at least one of these is off (probably the da6ng really)
Standard approach: manual dispersal matrix
Distances
Geographic distance = Great Circle Distance between area centroids !(rescaled by dividing by min. observed distance)
!
Environmental distance = Difference in absolute value of la7tude
Let’s try it. !
Phylogeny: Zanne et al. (2013), Nature, 15,000+ angiosperms !
Geography: median lat/long of species ranges !
Regions: Realms x Biomes (58 regions total) !
Assump7on: everything lives in 1 area
New approach: es7mate dispersal matrix
Realms x Biomes
Realms x Biomes
Realms x Biomes
Realms x Biomes
Realms x Biomes
Model comparison
Base model: BAYAREALIKE-d-e!+a means base rate of dispersal!+x means dispersal prob. modified by distance^x!+n means dispersal prob. modified by enviromental distance^n!+J means weight of cladogenetic jump dispersal!!Param.!LnL!+a!! ! -54459.68!
Model comparison
Base model: BAYAREALIKE-d-e!+a means base rate of dispersal!+x means dispersal prob. modified by distance^x!+n means dispersal prob. modified by enviromental distance^n!+J means weight of cladogenetic jump dispersal!!Param.!LnL!+a!! ! -54459.68!+a+x!! -50465.14 !
Model comparison
Base model: BAYAREALIKE-d-e!+a means base rate of dispersal!+x means dispersal prob. modified by distance^x!+n means dispersal prob. modified by enviromental distance^n!+J means weight of cladogenetic jump dispersal!!Param.!LnL! ! ! !+a!! ! -54459.68! !+a+x!! -50465.14 !+a+x+n!-49856.52 !!
Model comparison
Base model: BAYAREALIKE-d-e!+a means base rate of dispersal!+x means dispersal prob. modified by distance^x!+n means dispersal prob. modified by enviromental distance^n!+J means weight of cladogenetic jump dispersal!!Param.!LnL! ! ! a!! x! ! n!+a!! ! -54459.68! 0.002!+a+x!! -50465.14 0.157! ! -1.132!+a+x+n!-49856.52 2.021 !! -1.446! -0.473!!
Model comparison
Base model: BAYAREALIKE-d-e!+a means base rate of dispersal!+x means dispersal prob. modified by distance^x!+n means dispersal prob. modified by enviromental distance^n!+J means weight of cladogenetic jump dispersal!!Param.!LnL! ! ! a!! x! ! n!+a!! ! -54459.68! 0.002!+a+x!! -50465.14 0.157! ! -1.132!+a+x+n!-49856.52 2.021 !! -1.446! -0.473!!+J models -- no significant improvement (probably due to many missing species within genera?)
Model comparison
Base model: BAYAREALIKE-d-e!+a means base rate of dispersal!+x means dispersal prob. modified by distance^x!+n means dispersal prob. modified by enviromental distance^n!+J means weight of cladogenetic jump dispersal!!Param.!LnL! ! ! a!! x! ! n!+a!! ! -54459.68! 0.002!+a+x!! -50465.14 0.157! ! -1.132!+a+x+n!-49856.52 2.021 !! -1.446! -0.473!!+J models -- no significant improvement (probably due to many missing species within genera?)
Both distance and environmental distance have big effects on angiosperm dispersal
Looking at the global angiosperm macroevolu7onary dispersal kernel
Looking at the global angiosperm macroevolu7onary dispersal kernel
Looking at the global angiosperm macroevolu7onary dispersal kernel
Looking at the global angiosperm macroevolu7onary dispersal kernel
Looking at the global angiosperm macroevolu7onary dispersal kernel
Looking at the global angiosperm macroevolu7onary dispersal kernel
Looking at the global angiosperm macroevolu7onary dispersal kernel
Looking at the global angiosperm macroevolu7onary dispersal kernel
Biogeographical stochas7c mapping…
Biogeographical stochas7c mapping…mapping
Biogeographical stochas7c mapping…mapping
Biogeographical stochas7c mapping…mapping
1. Historical biogeography: What’s the point? ancestral ranges < learning about process
2. Models morghulis Models dohaeris
3. Models in BioGeoBEARS Test your hypotheses with model choice
4. Adding more realism with +x and +n Distance and environmental distance maRer!
5. Es6ma6ng the global angiosperm macroevolu6onary dispersal kernel
Outline
Acknowledgements Ques6ons/comments/collabora6ons at: [email protected] (also: seeking a job!)
Funding: NIMBioS NSF “Bivalves in Time and Space” UC Berkeley Wang Fellowship UC Berkeley Tien Fellowship Google Summer of Code NIMBioS
TRY IT YOURSELF AT: hMp://phylo.wikidot.com/biogeobears
Thanks especially to: !Jim Albert !NIMBioS Brian O’Meara Jeremy Beaulieu Ka?e Massana Michael Landis !Ph.D. commicee John Huelsenbeck Tony Barnosky David Jablonski Roger Byrne !Systema?c Biology editors & reviewers